Stability and dynamics of nonlinear excitations in a two-dimensional droplet-bearing environment

TL;DR

This paper investigates the stability and dynamics of nonlinear excitations like dark solitons, bubbles, and kinks in a two-dimensional droplet environment modeled by an extended Gross-Pitaevskii equation, revealing their stability regimes and destabilization mechanisms.

Contribution

It provides a comprehensive analysis of stationary states and their stability in a 2D droplet setting, combining reduced potential, Bogoliubov-de-Gennes, and variational methods, with experimental relevance.

Findings

Dark soliton stripes and bubbles can be destabilized via snake instability.

Droplets exhibit spectral stability in the studied environment.

Kinks are spectrally stable against transverse excitations.

Abstract

We unravel stationary states in the form of dark soliton stripes, bubbles, and kinks embedded in a two-dimensional droplet-bearing setting emulated by an extended Gross-Pitaevskii approach. The existence of these configurations is corroborated through an effectively reduced potential picture demonstrating their concrete parametric regions of existence. The excitation spectra of such configurations are analyzed within the Bogoliubov-de-Gennes framework exposing the destabilization of dark soliton stripes and bubbles, while confirming the stability of droplets, and importantly unveiling spectral stability of the kink against transverse excitations. Additionally, a variational approach is constructed providing access to the transverse stability analysis of the dark soliton stripe for arbitrary chemical potentials and widths of the structure. This is subsequently compared with the stability analysis outcome demonstrating very good agreement at small wavenumbers. Dynamical destabilization of dark soliton stripes via the snake instability is showcased, while bubbles are found to feature both a splitting into a gray soliton pair and a transverse instability thereof. These results shed light on unexplored stability and instability properties of nonlinear excitations in environments featuring a competition of mean-field repulsion and beyond-mean-field attraction that can be probed by state-of-the-art experiments.